Statistical Laws and Mechanics of Voronoi Random Lattices

TL;DR

This paper studies Voronoi-based random lattices with dynamic points, analyzing their statistical properties and laws through Monte Carlo simulations to understand their equilibrium behavior.

Contribution

It introduces a model of Voronoi random lattices with energy and investigates their statistical laws using Monte Carlo methods.

Findings

Coordination number distributions are characterized.

Aboav-Weaire and Lewis laws are tested.

Thermodynamic equilibrium properties are analyzed.

Abstract

We investigate random lattices where the connectivities are determined by the Voronoi construction, while the location of the points are the dynamic degrees of freedom. The Voronoi random lattices with an associated energy are immersed in a heat bath and investigated using a Monte Carlo simulation algorithm. In thermodynamic equilibrium we measure coordination number distributions and test the Aboav-Weaire and Lewis laws.